4 Summary

We have investigated the evolution of a mass-loaded wind blown bubble with a constant rate of injection of mechanical energy from a central wind source. The mass loading occurs due to the hydrodynamic ablation of distributed clumps, and is "switched-on'' at a specified radius, interior to which the wind expands freely. The requirement that the solution be self-similar imposes a link between the radial variation of the interclump density ( $\rho \propto r^{\beta}$) and the rate of mass loading from the clumps ( $\dot{\rho} \propto r^{\lambda}$) which forces $\lambda = (2\beta - 5)/3$.

We first produced solutions with negligible mass loading and $\beta=-2$(which correspond to constant $\dot{M}_{\rm wind}$ and $v_{\rm wind}$), which we compared with results obtained by Dyson (1973). Excellent agreement for the structure of the bubble was found. We also confirmed that for negligible mass loading, the value of $x_{\rm ml}$had no effect on the resulting solutions, as desired.

We then investigated the changes in the structure of the bubble for different values of $\lambda$, $\phi$, $x_{\rm is}/x_{\rm cd}$, and $x_{\rm ml}$. The central conclusions are:

• Substantial mass loading of the wind-blown bubble can occur over a wide range of $\lambda$. However, to additionally satisfy the requirement that the bubble mass is larger than the mass of the swept-up shell, low values of $\lambda$ are needed (e.g. ).
• The profiles of the flow variables are significantly altered under conditions of large mass loading. With respect to solutions with negligible mass loading, the density and temperature profiles increase, and the velocity and Mach number profiles drop. Changes to the profiles can be very rapid. Mass loading of the wind also reduces the Mach number prior to the inner shock.
• The mass-loaded wind may also connect directly to the contact discontinuity without the need for a global inner shock.
• The Mach number of the flow relative to the clumps which are injecting the mass can take several different forms. The flow can be either entirely supersonic, or have one (or maybe more) sonic points.
• Whilst mass loading reduces the bubble temperature, it also tends to reduce the emissivity in the interior of the bubble relative to its limb, whilst simultaneously increasing the central temperature relative to the limb temperature. The maximum temperature in the bubble is often not the post-inner-shock temperature, but occurs near the onset of mass loading. In some cases this can be many times greater than the post-inner-shock temperature.

Acknowledgements

JMP would like to thank PPARC for the funding of a PDRA position, and Sam Falle and Rob Coker for helpful discussions. We would also like to thank an anonymous referee whose suggestions improved this paper. This work has made use of Nasa's Astrophysics Data System Abstract Service.